ArrayPad unexpected changing of order

A way without ArrayPad

Join[{y, z}, Map[x &, Range[4]]]
(* Out: {y, z, x, x, x, x} *)

PadRight[{y, z}, 10, x]

First a function that gives the desired output:

ClearAll[arrayPad]
arrayPad = ArrayPad[#, {{0, 0}, {#3, 0}}, PadRight[#2, #3 + Length@#[[1]], #2]] &;

Examples:

Row[{Grid[Prepend[{#, {y, z}, 2,
     arrayPad[#, {y, z}, 2]} & /@ ({ ConstantArray[x, #]} & /@ Range[4]), 
    {"a", "padding", "m", "arrayPad[a,padding,m]"}], Dividers -> All],
  Grid[Prepend[{#, {y, z, w}, 3, 
       arrayPad[#, {y, z, w}, 3]} & /@ ({ ConstantArray[x, #]} & /@ Range[4]), 
    {"a", "padding", "m", "arrayPad[a,padding,m]"}], Dividers -> All], 
  Grid[Prepend[{#, Range[4], 5,
       arrayPad[#, Range[4], 5]} & /@ ({ ConstantArray[x, #]} & /@ Range[4]),
    {"a", "padding", "m", "arrayPad[a,padding,m]"}], Dividers -> All]}, Spacer[5]]

How come ArrayPad changes the ordering?

Trace @ ArrayPad[{{x}}, {{0, 0} , {2, 0}}, {y, z}]

{ArrayPad[{{x}}, {{0, 0}, {2, 0}}, {y, z}], 
 PadLeft[{{x}}, {1, 3}, {y, z}, {0, 0}], {{z, y, x}}}

PadLeft >> Details

That is, ArrayPad[{a}, {{0,0}, {m,0}}, padding] behaves as if it takes PadLeft[padding, m + Length[a], padding] and replaces the last Length[a] elements of this list with a. For the example in OP:

PadLeft[{y, z}, 2 + #, {y, z}] & /@ Range[3]

{ {z, y, z}, {y, z, y, z}, {z, y, z, y, z}}

whereas

PadRight[{y, z}, 2 + #, {y, z}] & /@ Range[3]

{{y, z, y}, {y, z, y, z}, {y, z, y, z, y}}

In other words, ArrayPad[a, {{0,0}, {m,0}}, padding] behaves like the version of arrayPad above with PadRight replaced with PadLeft:

padding = Range[5];
pl = RandomInteger[{1, 10}]; 

And @@ (ArrayPad[{ConstantArray[x, #]}, {{0, 0}, {pl, 0}}, padding] === 
  ArrayPad[{ConstantArray[x, #]}, {{0, 0}, {pl, 0}},
    PadLeft[padding, pl + #, padding]] & /@ Range[10])

 True